Time reversal symmetry for classical, non-relativistic quantum and spin systems in presence of magnetic fields

• Published in: Annals of physics Vol. 441; p. 168853
• Main Authors: Carbone, Davide, De Gregorio, Paolo, Rondoni, Lamberto
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2022
• Subjects: Invariance; Magnetic field; Onsager relation; Spin; Symmetry transformation; Time reversal; Onsager relation; Symmetry transformation; Invariance; Spin; Magnetic field; Time reversal
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2022.168853

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations and the so-called fluctuation theorems, are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are non-relativistic, and are described by the Schrödinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases. These results are relevant for experiments such as diffusion in solutions, thermoelectricity and spin charge transport. Indeed, no violation of the Onsager relations has been found in presence of a magnetic field, contrary to general expectations. •Time reversal symmetry hold also for systems subject to an external magnetic field•Time reversal operations are applied to non-relativistic quantum spinless and spin systems in a magnetic field•Onsager reciprocal relations and fluctuation relations hold in classical and quantum systems in external magnetic fields, under the validity of mild compatibility conditions•Different generalized time reversal symmetries can be simultaneously used to impose constraints on response tensors